Generalized oscillator strength for the3s-3ptransition in sodium

Solutions of the close-coupling equations are obtained for sodium in a four-state approximation (3s,3p,4s,3d) at energies of 22.1, 54, and 150 eV. Generalized oscillator strengths (GOS) deduced from the resulting differential cross sections for the 3s-3p transition are plotted as a function of momentum transfer squared (K²). The resulting GOS do not tend to the exact value of the optical oscillator strength as K² goes to 0, thus violating Lassettre's hypothesis. While Lassettre's theorem is not satisfied exactly, the concepts underlying this hypothesis are still useful at sufficiently high energies.